Reinforcement learning with action consisting of two discrete values
You would still be picking a single action. Your action space is now $\mathcal{A} = \mathcal{O} \times \mathcal{I}$ where I've chosen $\mathcal{O}$ to be the set of possible orders from your problem and $\mathcal{I}$ to be the set of possible items.
Provided both of these sets are finite, then you should still be able to approach this problem with DQN. Theoretically, this should be easy to see, as any element from $\mathcal{A}$ is still a single element it just happens that this element is now a tuple.
From a programming point of view, let's consider the simple example of cartpole, where the possible actions are left and right. Your $Q$-function obviously won't know the meanings of 'left' and 'right', you just assign it to an element of a vector, i.e. your $Q$-function would output a vector in $\mathbb{R}^2$ with e.g. the first element corresponding to the score for 'left' and the second element corresponding to the score for 'right'. This is still the case in your problem formulation, you will just have a $Q$-function that outputs a vector in $\mathbb{R}^d$ where $d = |\mathcal{A}|$ - you would just have to make sure you know which element corresponds to which action.
Also, there is the possibility that this approach could leave you with a large dimensional vector output, which I imagine would probably mean you'd need more simulations to properly explore the action space.
Hope this helps.